Factors Affecting the Weakening Rate of Tropical Cyclones Over the Western North Pacific

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Factors Affecting the Weakening Rate of Tropical Cyclones over the Western North Paciﬁc

RONG FEI State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, China Meteorological Administration, and College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China, and International Paciﬁc Research Center, and Department of Atmospheric Sciences, University of Hawai‘i at Manoa, Honolulu, Hawaii

JING XU State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, China Meteorological Administration, Beijing, China

YUQING WANG International Paciﬁc Research Center, and Department of Atmospheric Sciences, University of Hawai‘i at Manoa, Honolulu, Hawaii, and State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, China Meteorological Administration, Beijing, China

CHI YANG College of Global Change and Earth System Science, Beijing Normal University, Beijing, China

(Manuscript received 29 October 2019, in ﬁnal form 23 June 2020)

ABSTRACT

In this study, based on the 6-hourly tropical cyclone (TC) best track data and the ERA-Interim reanalysis data, statistical analyses as well as a machine learning approach, XGBoost, are used to identify and quantify factors that affect the overwater weakening rate (WR) of TCs over the western North Paciﬁc (WNP) during 1980–2017. Statistical analyses show that the TC rapid weakening events usually occur when intense TCs cross regions with a sharp decrease in sea surface temperature (DSST) with relatively faster eastward or northward translational speeds, and move into regions with large environmental vertical wind shear (VWS) and dry conditions in the upshear-left quadrant. Results from XGBoost indicate that the relative intensity of TC (TC intensity normalized by its maximum potential intensity), DSST, and VWS are dominant factors determining 2 2 TC WR, contributing 26.0%, 18.3%, and 14.9% to TC WR, and 9, 5, and 5 m s 1 day 1 to the variability of TC WR, respectively. Relative humidity in the upshear-left quadrant of VWS, zonal translational speed, divergence at 200 hPa, and meridional translational speed contribute 12.1%, 11.8%, 8.8%, and 8.1% to TC WR, 2 2 respectively, but only contribute 2–3 m s 1 day 1 to the variability of TC WR individually. These ﬁndings suggest that the improved accurate analysis and prediction of the dominant factors may lead to substantial improvements in the prediction of TC WR.

1. Introduction TC events, such as the rapid intensiﬁcation (Tao et al. 2017; Jiang et al. 2018; Knaff et al. 2018) and the intensity Intensity prediction of tropical cyclones (TCs) is change associated with eyewall replacement cycles in TCs known to be challenging in operational TC forecasts (Kossin and Sitkowski 2012; Kossin 2015; Kossin and (e.g., Elsberry et al. 2007; Kaplan et al. 2010). In the last DeMaria 2016). However, less studies have focused on decade or so, many efforts have been devoted to under- the weakening process of TCs in the literature. TC standing crucial issues in the predictability of intensifying weakening, especially rapid weakening (RW), is one of the major sources of large intensity forecasting errors. 2 Corresponding author: Dr. Jing Xu, [email protected] RW is often deﬁned as a decrease of 30 kt (15.4 m s 1)or

DOI: 10.1175/MWR-D-19-0356.1 Ó 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 09/30/21 12:08 PM UTC 3694 MONTHLY WEATHER REVIEW VOLUME 148 more in sustained near surface wind speed in 24 h when As a small-probability event of TC weakening, TC the TC is over open water (Wood and Ritchie 2015). RW is often defined as the bottom 5% of all TC intensity Statistical analyses show that the positive errors in official change rates (e.g., Wood and Ritchie 2015; Ma et al. intensity forecast are often related to the TC-weakening 2019). Wood and Ritchie (2015) showed that TC RW cases, that is, their intensities are often overpredicted in always occurred when a TC crossed a sharp SST gradi- official forecasts, especially for RW events (Wood and ent, encountered strong VWS, or experienced dry air Ritchie 2015; Na et al. 2018). The overpredicted intensity intrusion over the North Atlantic and the eastern forecast during the TC weakening stage may lead to North Pacific. They found that these inhibiting envi- overestimation of TC destructive potential and false ronmental factors contribute either individually or alarm. Therefore, understanding of TC weakening pro- jointly to TC RW; decreasing SST and increasing cesses is of great importance to improve TC intensity VWS contribute the most over the North Atlantic, forecasting and destructive potential estimation. while decreasing SST and low low-level relative hu- TCs often form over warm tropical oceans with sea midity contribute the most in the eastern North surface temperature (SST) over 26.58C under favorable Pacific. More recently, Ma et al. (2019) drew some environmental atmospheric conditions, such as weak similar conclusions on the dominating effect of VWS environmental vertical wind shear (VWS) and a moist and sharp SST gradient on TC RW over the western midtroposphere (Gray 1968). After their formation, North Pacific (WNP). However, they found that the TCs generally intensify and move away from the deep effect of midlevel dry-air intrusion was insignificant tropics. Some oceanic and atmospheric environmental during RW over the WNP compared with that in the conditions may become unfavorable for a TC to inten- North Atlantic and eastern North Pacific. They pro- sify or even maintain its intensity, and thus the TC may posed that this may be due to the lack of prevailing experience its weakening phase. Among those condi- midlevel dry-air layer (such as the Saharan air layer tions, SST is the most important factor influencing TC over the North Atlantic) over the WNP. The monsoon intensity change because it largely determines the en- gyres are another special environmental factor that ergy supply to a TC through surface enthalpy flux from can induce TC RW over the tropical WNP. Liang et al. the underlying ocean. SST also is one of the key pa- (2018) found that more than 40% of RW events south rameters that determine the maximum potential inten- of 258N were associated with the monsoon gyres. They sity (MPI) of a TC (Miller 1958; Emanuel 1986, 1988, suggested the monsoon gyres affect TC RW by mod- 1995, 1997; Holland 1997). In addition to SST, envi- ulating the TC structure. ronmental atmospheric conditions may largely modu- Most previous studies have focused on individual late the TC intensity, such as VWS in the environmental factors influencing TC weakening or some weakening flow (e.g., DeMaria and Kaplan 1999; Zeng et al. 2007, cases, or on composite analyses of environmental fac- 2008, 2010; Wang et al. 2015; Bukunt and Barnes 2015) tors in classified TC intensity changes (such as RW and and dry air in the near-core TC environment (Hendricks non-RW) qualitatively. A systematic analysis of TC et al. 2010; Davis and Ahijevych 2012; Fowler and weakening rate (WR) as a continuous response and its Galarneau 2017; Juracic´ and Raymond 2016). Strong relationship with the associated environmental factors VWS can lead to the weakening of a TC through ven- over the WNP has not been conducted yet. The main tilating the warm core, diluting moist air in the eyewall, objectives of this study are 1) to present the climato- and inducing large asymmetries in the inner core (Gray logical characteristics of all overwater TC weakening 1968; Frank and Ritchie 2001; Tang and Emanuel 2010, cases, especially RW cases, over the WNP, 2) to identify 2012; Riemer et al. 2010, 2013; Xu and Wang 2013; Fu the dominant environmental factors that affect TC WR, and Wang 2017). Dry air in the near-core TC environ- and 3) to quantify the relative contributions of envi- ment can lead to TC weakening if the dry air is entrained ronmental factors to TC WR through sensitivity analysis into the eyewall updraft to promote strong downdrafts, based on a machine learning approach, the XGBoost especially when large VWS exists (Davis and Ahijevych method. The rest of this paper is organized as follows. 2012; Fowler and Galarneau 2017). Moreover, some Section 2 describes the data and methods used in this internal processes may also lead to TC intensity change, study. The basic climatological characteristics of TC such as the development of strong outer spiral rainbands weakening and RW are given in section 3. The envi- (Wang 2009) or the formation of a secondary eyewall ronmental factors that significantly affect TC WR are and the related eyewall replacement cycle (Willoughby identified in section 4. The relative importance of vari- et al. 1982; Houze et al. 2007; Sitkowski et al. 2011; ous environmental factors to TC WR is analyzed and Kossin and Sitkowski 2012; Yang et al. 2013; Kossin discussed in section 5. The main findings are summa- 2015; Kossin and DeMaria 2016). rized in the last section.

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TABLE 1. The factors analyzed in this study with their units and descriptions.

Variables Unit Description 2 Vmax m s 1 Initial TC intensity, calculated by subtracting 40% of SPD from the maximum wind speed in the best track data SST 8C Initial sea surface temperature averaged within a radius of 300 km from the TC center POT Relative intensity, calculated as initial intensity divided by the corresponding MPI DSST 8C SST change within 24 h along TC track 2 SPD m s 1 Translational speed of the TC center 2 USPD m s 1 Zonal translational speed of the TC center 2 VSPD m s 1 Meridional translational speed of the TC center 2 VWS m s 1 Area-averaged (200–800 km) 200–850-hPa vertical wind shear 2 DIV200 s 1 Divergence averaged within a radius of 1000 km from the TC center at 200 hPa RHUL % Area-averaged (between 200 and 800 km radii) and vertically averaged (300–850 hPa) relative humidity in the upshear-left quadrant RHUR % As in RHUL, but in the upshear-right quadrant RHDL % As in RHUL, but in the downshear-left quadrant RHDR % As in RHUL, but in the downshear-right quadrant

2. Data and methods in our analysis. In addition, to avoid the effect of short-term fluctuations in TC intensity, following Wood and Ritchie a. Data (2015), weakening cases with any 6-hourly intensification Persistence and environmental variables used in this within a 24-h window were also excluded. 2 study are listed in Table 1. The Joint Typhoon Warning As in Wood and Ritchie (2015), a 30 kt (15.4 m s 1) Center (JTWC) best track dataset for WNP TCs during decrease in Vmax in 24 h was chosen as the threshold to 1980–2017 was obtained from the IBTrACS version 4 define an RW case in this study. We used the magnitude of (Knapp et al. 2010, 2018). The period since 1980 is decrease in Vmax in 24 h to quantify the WR (without a generally considered the modern era, because geosta- negative sign). Accordingly, slow weakening (SW) cases tionary satellite coverage has been nearly global and were defined as weakening cases with WR less than the polar orbiting satellite data has been more widely RW threshold. In addition, TCs that experienced RW available than previous years. Uncertainties in TC in- were simply called RW TCs and those non-RW TCs were tensity and position estimations have been largely re- called SW TCs. A total of 475 TCs with 3108 weakening duced since then (https://www.ncdc.noaa.gov/ibtracs/pdf/ cases, among which there were 153 RW TCs with 434 RW IBTrACS_version4_Technical _Details.pdf). The dataset cases, were included in our following analyses. includes 6-hourly TC location and maximum 1-min mean The 6-hourly environmental data, including horizontal sustained surface wind speed. Only storms with tropical winds, relative humidity (RH) and SST, was derived from nature are included in our analysis. More than 95% of their the European Centre for Medium-Range Weather 50-kt wind radii are less than 200 km. Since the TC inner- Forecasts (ECMWF) interim reanalysis (ERA-Interim), core can be fully covered by the 50-kt wind radius, TC cases with a horizontal resolution of 0.75830.758 and at 37 with the storm center within 200 km from any landmass pressure levels (Dee et al. 2011). The wind fields were fil- were excluded to avoid intensity change caused by signifi- tered beforehand to remove all disturbances, including cant topographic (including land) effects. Due to the con- TCs, with wavelengths less than 1000 km based on the tribution of a storm’s translational speed (SPD) to the algorithm described in Kurihara et al. (1993). Specifically, maximum wind speed of the storm, the initial maximum the filtering algorithm is a local three-point smoothing wind speeds in the best track data cannot represent the operator applied iteratively in both the zonal and me- purely circular component of maximum wind speeds. ridional directions. The TC environmental zonal wind Therefore, to minimize the influence of storm translation (U) and meridional wind (V)weredefinedastheaverage on storm intensity, we subtracted 40% of the storm trans- over an annulus between radii of 200 and 800 km from the lational speed from the initial maximum wind speed for all TC center, and VWS between 200 and 850 hPa were then TC cases and used the result as the measure of TC intensity calculated accordingly using the averaged environmental (Vmax), as done by Emanuel et al. (2004). The TC intensity U and V. Note that this deep-layer shear is a good indi- changes at 24-h intervals were calculated accordingly. Cases cator of environmental VWS effect on TCs and is widely with intensity change in 24 h less than zero were defined as used in the study of TC intensity change (e.g., Zeng et al. weakening cases. Only TCs with their centers south of 408N 2010; Wang et al. 2015). Large-scale divergence at 200 hPa while experiencing their weakening stages were considered (DIV200) was defined as the average of divergence in a

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V 5 1 T 2 radius of 1000 km from the TC center. The SST of each TC the target yi; ( fk) gT 1/2låj51wj , l and g are the case was defined as the average in a radius of 300 km from regularization parameters. The second term V penalizes the TC center. The above calculations all followed those the complexity of the model. The additional regulari- used in SHIPS model (DeMaria and Kaplan 1999). The zation term helps to smooth the final learned weights to TC MPI was estimated using the algorithm described in avoid overfitting. As a result, while achieving high ac- Bister and Emanuel (2002). curacy in representing the training cases, XGBoost exhibits great generalization ability to predict new cases. b. The XGBoost methods In addition, XGBoost provides a natural measure of An effective machine learning method called extreme feature importance. Importance is a relative score that gradient boosting (XGBoost) (Chen and Guestrin 2016) indicates the fractional contribution of each feature to was used to quantitatively evaluate the relative contri- the model performance measure, and is 100% when (t21) g 5 › 2 l y y^ butions of environmental factors to TC WR. XGBoost summed over all features. Denote i y^(t 1) ( i, ) 2 (t21) is an implementation of gradient tree boosting (GTB) and hi 5 › l(yi, y^ ) for the ith case at the tth iter- y^(t21) (Friedman 2001), one ensemble learning technique that ation in boosting the minimization of Eq. (2). For the has been used in many applications. Tree-based methods split on a feature, assume that IL and IR are the case sets partition the feature space into a set of rectangles (leaves) of the left and right nodes after the split. It can be shown through recursive binary splitting, and then fit a simple that the approximate loss reduction, or the ‘‘gain,’’ after model (e.g., a constant mean) in each one (Breiman et al. the split is given by 1984). The feature space partition is fully described by a " # 2 2 (G 1 G )2 single tree (also known as classification and regression 5 1 GL 1 GR 2 L R 2 Gain 1 1 1 1 g , (3) tree, or CART). Essentially, a tree is a piecewise constant 2 HL l HR l HL HR l or linear regression model. For a given dataset D with n cases and m features, 5 (x , y ) (x Rm, y R, where G 5 å g , G 5 å g , H 5 å h ,and D f i i g i 2 i 2 L i2IL i R i2IR i L i2IL i i 5 1, ... , n), a tree ensemble model uses K additive H 5 å h . Feature importance is calculated by first R i2IR i functions (trees) to predict the output: summing the gain of this feature’s splits within a single tree, weighted by the number of related observations, K ^ 5 5 å and then averaged across all of the trees within the yi f(xi) fk(xi), fk 2F, (1) k51 model. Once the model is fitted, importance is also evaluated accordingly for each feature. Even for a case 5 5 Rm / RT where F f f (x) wq(x)g (q: T, w 2 )isthe where there are highly correlated features, XGBoost space of regression trees, q represents the structure of each can also provide reliable estimates of importance for at tree that maps a case to the corresponding leaf index, T is least one of them, unlike in the multivariate linear the number of leaves in the tree, each fk corresponds to an models where their statistical significance could be ‘‘di- independent tree structure q and leaf weights w. Typically, luted’’ such that none of them would pass the signifi- additive models with a form as in Eq. (1) are fitted by cance test (Chen and Guestrin 2016). minimizing a loss function averaged over the training data, Because of the above advantages, XGBoost has been such as the squared-error or a likelihood-based loss func- successfully applied to investigate the nonlinear relation. However, for the tree ensemble model, it is difficult tionships between the response and features of a com- to train using traditional numerical optimization tech- plex system. The fitted model itself is much like a proxy niques. Instead, the model can be trained in an additive model that encodes such relationships. To reveal a re- manner, known as GTB. The number of additive trees K lationship of interest, visualization methods, such as increases iteratively to make the value of loss function partial dependence plot (PDP) (Friedman 2001) and in- smaller and smaller. For a comprehensive introduction to dividual conditional expectation (ICE) plots (Goldstein CART and boosting methods, please refer to Hastie et al. et al. 2015), are usually applied. In practice, ICE is a series (2009),chapters9and10. of model-predicted response curves, generated by vary- XGBoost trains the set of functions used in Eq. (1) by ing the feature of interest over its value range while minimizing the following regularized objective using GTB: keeping the others fixed as observed for each training case. PDP is just the average curve of ICE curves over all n K cases. Other statistics of ICE, such as the quartiles, can L(f) 5 å l( y^ , y ) 1 å V( f ), (2) i i k also be plotted to reveal the variability of the response i51 k51 at the given value of the feature of interest. Take VWS as where l is a differentiable convex loss function that the example feature of interest. For each RW case, we ^ measures the difference between the prediction yi and can use the fitted model to predict TC WR for each of

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finely discretized values over the observed VWS range in turn, with all the other features fixed as observed. The ICE curve for each case is then achieved by linking the predicted values. If the feature of interest is almost independent of the other features, then its ICE curves as well as its PDP and quartile curves are approximately parallel (the interquartile range does not change with the feature). Otherwise, ICE curves may cross and their interquartile range may change with the feature, implying that the feature interacts with some of or all the others. It should be noted that for regression problems as we will deal with in section 5, each tree in the XGBoost model comprises of local linear regressions for individual leaves on the tree. Therefore, the ICE curves are zigzagged in nature. Since linear regressions are sensitive to outlier data, leaves containing outlier data might contribute to remarkable jumps on the predicted curves, as we will see in section 5b. In this study, we use the XGBoost method to establish an empirical model of TC WR using all identified dominant environmental factors. It should be men- tioned that, unlike SHIPS or other related models, here the fitted model is not used for forecasting. Instead, it serves as an analysis tool to investigate the nonlinear relationships between TC WR and various factors. The relative importance of these factors is evaluated accordingly. Sensitivity and variability of TC WR in response to these individual factors are investigated using the ICE method based on the fitted model.

3. Characteristics of TC weakening over the WNP

Figure 1a shows the spatial distribution of TC WR and 21 21 FIG. 1. (a) Spatial distributions of TC WR (shaded, m s day ) 83 8 the frequency of weakening cases in each 2.5 2.5 grid and weakening case frequency (contour) in each 2.5832.58 grid box in typhoon seasons (from June to November) during box in typhoon seasons (from June to November) during 1980– 1980–2017 over the WNP. It shows that most of the 2017. (b) Tracks of RW TCs in their lifetimes, note that the overwater weakening cases are located in the region of weakening stages are shown as white curves and the RW (SW) 8 8 8 8 8 8 stages of RW TCs are marked as black (gray) curves, with the 15 –35 N, 125 –160 E and centered near 22 N, 130 E. underlying shade denotes climatologically mean SST in typhoon 8 Higher WR usually occurs north of 20 N. This is because seasons. (c) As in (b), but for SW TCs. TCs often experience their major weakening phase at latitudes north of 208N after their intensiﬁcation stages. Moreover, unfavorable environmental condi- with the results of Ma et al. (2019), who also found that tions at midlatitudes may enhance the WR of TCs. Note the RW cases usually occur as TCs crossed a sharp SST that there is a local maximum in WR just off the coast of gradient over the WNP. Japan, which is due to the relatively high WR of only one Note that few RW TCs were observed in the South case falling in that grid box. Figures 1b and 1c show RW China Sea (SCS) in our analysis. This is mainly due to TC and SW TC tracks, respectively. The SW stages relatively few strong TCs over the SCS, and the warm during RW TC lifetimes are indicated as gray, while SST greater than 288C in SCS is also unfavorable for TC the RW stages are highlighted as black. The RW weakening (Figs. 1b,c). Only TCs that formed in the SCS stages usually start at the recurving points of TC tracks were counted, while those that entered the SCS after northward or northeastward, which is probably related landfall but formed outside the SCS were not included in to the sharp decrease in SST along the TC tracks or/and our analysis. Note also that some RW TCs occurred in the change in environmental wind ﬁeld. This is consistent the tropical WNP, which should be related to monsoon

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FIG. 2. Monthly variations of (a) all weakening TCs (gray) and RW TCs (black), and the ratio of RW TCs to total weakening TCs (curve), and (b) all weakening cases (gray) and RW cases (black), and the ratio of RW cases to total weakening cases (curve) from June to November during 1980–2017. The corresponding numbers are also given at the tops of their corresponding bars. gyres as recently studied by Liang et al. (2018). They with atmospheric variations as well, such as drier mid- found that although less than one-third of RW events troposphere and stronger vertical wind shear in fall than occurred south of 258N, more than 40% of them were in summer. associated with monsoon gyres over the WNP. They Table 2 compares the statistics of SW and RW TCs showed that about 85% of these RW events were usually as a function of the weakening duration. Here we define observed near the center of a monsoon gyre when a TC the weakening duration as a period of ongoing weak- made a sudden northward turn. Comparing Figs. 1b ening without any intensification of each TC, calculated and 1c, we can see that there are no distinct differences as a continuous and overlapping 24-h weakening period. in geographical distribution between the RW and SW It is different from a weakening case, which refers to the TC tracks, particularly in the high WR regions north of weakening over a 24-h period. The average weakening 258N, although the initial stages of SW TCs were farther duration (including both SW and RW TCs) is 67 h per southward than those of RW TCs. This suggests that the TC. The frequency of weakening TCs decreases with two groups of TCs were governed by other factors, such increasing weakening duration. TCs with their weak- as persistence and/or environmental factors. ening duration more than 6 days account for only 6.2% Figure 2 displays the monthly distributions of the of total TCs. Comparing the weakening duration of RW numbers of total weakening TCs and RW TCs (Fig. 2a), and SW TCs, we can find that TCs experiencing RW and the numbers of total weakening cases and RW cases periods usually have slightly longer weakening duration (Fig. 2b), as well as their respective ratios. Here a than those only experiencing SW in their lifetimes. The weakening case refers to a 6-hourly observation of a TC average weakening duration of RW TCs is 82 h, while with a decrease in Vmax in 24 h, while a RW case is a that of SW TCs is only 62 h. Totally, 434 RW cases from 2 weakening case with a decrease of at least 15.4 m s 1 in 153 RW TCs occurred in the WNP. This means that on Vmax in 24 h. It can be seen that the numbers of both average each RW TC produces about 3 overlapping RW RW TCs and RW cases increase from June to October, cases, or equivalently, each RW TC experiences the RW with 31 RW TCs out of total 87 TCs (36%) and 82 RW period of about 36 h since the TC best track records used cases out of 555 weakening cases (15%), respectively, in in the analysis are 6-hourly. This is comparable with the October. However, the ratio of RW TCs to all TCs and 36 and 30 h of average RW durations in the eastern that of RW cases to all weakening cases increase sig- North Pacific and North Atlantic, respectively, reported nificantly from 14% (15 out of 110 TCs) and 5% (33 out in Wood and Ritchie (2015). of 675 weakening cases) in August to 49% (19 out of TCs that experienced long RW durations usually 39 TCs) and 25% (62 out of 250 weakening cases) in have a relatively high lifetime maximum intensity November. In general, TC RW occurs more frequently (LMI). As we can see from Table 2, RW TCs with in fall than in summer over the WNP, which is likely to weakening duration longer than 48 h have an average 2 be associated with the lower MPI resulting from the LMI over 56 m s 1, while the averaged LMI of SW TCs lower SST in fall than in summer (Ge et al. 2018), and with weakening duration longer than 48 h is only

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TABLE 2. Statistics of RW and SW TCs for all and each interval of weakening duration (h) during 1980–2017: number of TCs (No.), averages of weakening duration [Avg weakening duration; (h)], RW duration (Avg RW duration; (h)], proportion of RW duration to 2 weakening duration (Avg proportion; %), and lifetime maximum intensity (Avg LMI; m s 1).

RW TCs SW TCs Weakening Avg weakening Avg RW Avg Avg Avg weakening Avg duration No. duration duration proportion LMI No. duration LMI [24–48) 33 34 28 0.83 54.1 138 30 35.8 [48,72) 39 57 37 0.66 56.8 80 56 36.8 [72,96) 29 81 42 0.52 66.0 47 81 38.6 [96–120) 20 106 40 0.38 65.8 25 102 53.7 [120–144) 18 130 39 0.30 63.1 13 130 50.9 [144–168) 6 155 40 0.26 69.9 8 150 67.3 [168–192) 5 176 41 0.23 65.8 9 180 56.1 [192–216) 3 196 40 0.20 68.9 2 210 58.1 All 153 82 37 0.55 60.9 322 62 39.9

2 36 m s 1. Note that three TCs weakened for more than ratio of the current TC intensity to its theoretical MPI, 192 h (8 days): KIM (1986), ELE (2002), and IOKE namely Vmax/MPI, hereafter POT), 24-h SST change (2006). KIM and IOKE experienced RW periods after along TC track (DSST), zonal and meridional transla- 2 they reached their LMIs of 67.8 and 70.4 m s 1,respec- tional speeds (USPD and VSPD) of all weakening TC tively. ELE experienced its relatively high maximum WR cases, together with their corresponding fitted 50th, 2 2 2 of 13.4 m s 1 day 1 afterpeakingitsLMIof57.5ms 1. 75th, and 95th percentiles of WRs. All the fitted per- Further analysis indicates that the weakening phases of centiles of TC WRs increase with increasing Vmax about 34% RW TCs (52 out of 153) lasted for longer than (Fig. 3a), showing an approximately linear dependence 96 h in the WNP. For RW TCs with weakening duration of TC WR on Vmax. Very few RW cases occur for 2 shorter than 60 h, the RW periods are mostly (85.8%) storms with intensity less than 35 m s 1 because tropical consecutive, while for the others whose weakening dura- storms (TS) are too weak to reach the RW threshold of 2 2 tion was longer than 60 h among RW TCs, most (73.3%) of 15.4 m s 1 day 1. The significant linear correlation be- them are discontinuous. Moreover, there are 86.1% (409 tween TC WR and Vmax (r 5 0.37) (Table 3) indicates out of 475) of TCs undergoing their first weakening phase, that Vmax is an important factor determining the sub- and about 29.4% (45 out of 153) of RW TCs undergoing sequent WR. Namely, a TC with a greater intensity at theirfirstRWperiodwithin24haftertheyreachedtheir and after it reaches its LMI tends to have a greater WR. LMIs. This indicates that only a minority of TCs in the WNP could maintain very high intensities after their LMIs for an appreciable period. This is probably because when TABLE 3. List of correlation coefficients between TC WR and a TC developed to a high intensity, it had already moved various parameters. The p values denote the statistical confidence of the corresponding correlation coefficient. Considering the case- to a less favorable environment than before, such as cooler size dependency [p value (C)] with 6-hourly data, p values based on SST, stronger vertical wind shear and drier midtropo- the degree of freedom with TC number are shown as p value (T). sphere. The detailed roles of the environmental factors will Correlation coefficients that are statistically significant above 99% be further examined in the next section. confidence level for p value (T) are set boldface. Parameters Correlation coef p value (C) p value (T) 4. Factors affecting TC weakening rate Vmax 0.37 00 2 2 SST 20.16 5.2 3 10 14 4.5 3 10 4 Weakening is often the last stage of a TC and mostly POT 0.40 00 2 occurs when the storm moves out of the deep tropics and DSST 20.26 0 8.3 3 10 9 2 enters a less favorable environment. In this section, we SPD 0.22 0 1.2 3 10 6 2 USPD 0.29 0 1.1 3 10 10 discuss factors affecting the TC overwater WR, includ- 2 VSPD 0.26 0 8.3 3 10 9 ing both the TC persistence variables and large-scale 2 VWS 0.29 0 1.1 3 10 10 2 environmental variables (Table 3). DIV200 0.07 9.4 3 10 5 0.13 2 RHUL 20.26 0 8.3 3 10 9 a. Persistence factors and SST 2 RHUR 20.08 8.0 3 10 6 0.08 Figure 3 shows the scatter diagrams of the 24-h WR RHDL 20.02 0.26 0.66 2 3 25 against Vmax, SST, relative intensity (defined as the RHDR 0.07 9.4 10 0.13

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FIG. 3. Scatter diagrams of TC WR against (a) Vmax, (b) SST, (c) POT (relative intensity; Vmax/MPI), (d) DSST, (e) USPD, and (f) VSPD. The ﬁtted 95th, 75th, and 50th percentiles of WR are shown as black, green, and red curves, respectively, and the curves are obtained using smoothed cubic spline approximation.

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This could be due to the fact that an intense TC typically that TC WR increases with the decrease in SST (viz., experiences a relatively long intensification stage, often negative DSST). The negative correlation of TC WR moves out of deep tropics (Fig. 1), and is about to enter with DSST (r 520.26) is higher than that with SST regions with decreasing SST or environmental atmo- (Table 3), suggesting that the greater decrease in SST spheric conditions unfavorable for TCs to maintain high can result in higher TC WR. This is consistent with the intensity. fact that most RW cases occurred for TCs crossing a The underlying SST largely determines the surface sharp SST gradient in the WNP (Fig. 1b). enthalpy flux in the inner core of a TC and thus is a key The SPD of a TC is also considered a factor affecting factor affecting TC intensity change. As we can see from TC intensity change (Zeng et al. 2007, 2008). Previous Fig. 3b, TC WR is negatively correlated with SST studies have shown that too low SPD is unfavorable for (r 520.16) (Table 3). In particular, the fitted 95th rapid intensification because of the negative feedback percentile shows an obvious decreasing trend of the from the cooling SST induced by upwelling (e.g., Walker upper bound of TC WR with increasing SST, confirming et al. 2014). However, a fast movement is unfavorable that SST is an important factor contributing to TC WR. for TC intensification likely due in part to the generation 2 2 Note that large TC WR higher than 30 m s 1 day 1 oc- of large asymmetries in the TC inner-core structure curs over SST between 26.58 and 28.58C rather than the (Peng et al. 1999; Zeng et al. 2007, 2008). As a result, we coldest SST (Fig. 3b). This is because TCs at relatively can consider that fast movement may favor TC RW, that low SSTs are often already weak so that their WRs could is, WR may increase with increasing SPD. This tendency not be too large. is clear in both Figs. 3e and 3f, which show the rela- Since current Vmax and SST are both important for tionships between TC WR and its fitted quantiles against the subsequent WR, and SST is a key parameter deter- USPD and VSPD, respectively. Both USPD and VSPD mining the TC MPI, we further examine the relationship are positively correlated with TC WR, with their cor- between TC WR and POT (Fig. 3c). POT represents relation coefficients being 0.29 and 0.26, respectively how far the current TC intensity is from its MPI. Similar (Table 3). This means that the TC WR becomes higher to Vmax, POT is also positively correlated with TC WR when a TC moves eastward and/or northward. This is (r 5 0.4) (Table 3). This implies that TCs with their in- also consistent with the fact that most RW TCs occur tensities closer to MPI may weaken more rapidly. The after they recurve northward and northeastward and greater POT indicates either stronger intensity or lower enter the midlatitude westerlies as shown in Fig. 1b. MPI, or both, which provides relatively greater potential Note that the RW TCs also occur in the region where for a TC to weaken. Particularly, greater POT implies SST decreases rapidly along the TC tracks, as we can see that the real upper limit of intensity will drop below the in Fig. 1b. Therefore, contributions to the positive cor- current intensity more easily and considerably when a relation of TC WR and SPD are not only from the fast TC encounters detrimental environmental conditions, translation itself, but also from other related changes in such as strong vertical wind shear and dry middle SST and atmospheric environment, such as VWS, as we troposphere. Note that there are about 12.9% of the will discuss further in section 5. weakening cases with POT greater than 1.0, imply- Figure 4 compares the frequency and cumulative ingthatsomeTCsaresuperintense(Persing and percentage distributions of SW and RW cases against Montgomery 2003). This is not unusual because ob- several factors discussed above. The RW cases mostly 2 servations did show that real TCs could have intensity occur in TCs with Vmax between 40 and 65 m s 1, ac- higher than their corresponding theoretical MPIs (e.g., counting for 71.4% of RW cases; whereas 90.8% of SW Montgomery et al. 2006). This could also happen when cases are evenly distributed in TCs with Vmax lower 2 a TC moves quickly to pass over cold water (because of than 65 m s 1 (Fig. 4a). The cumulative percentage dis- limited time for the storm to adjust to its environment; tributions show that 80% and 50% of RW cases occur 2 Emanuel 2000). with Vmax higher than 42 and 52 m s 1, respectively, The change in SST along the subsequent TC track while those of SW cases occur with Vmax higher than 24 2 could be a better indication of the energy input from the and 40 m s 1, respectively. The RW cases tend to occur underlying ocean to the TC than SST under the current at colder SST than the SW cases do, with the highest TC location. Therefore, it is expected that the TC WR frequency of RW and SW cases occurring at 27.58 and would be correlated with the decrease in SST more 28.58C, respectively (Fig. 4b). The majority (82.3%) of closely than with the SST itself. This is indeed the case as RW cases occur when POT is greater than 0.7, with their we can see in Fig. 3d, which shows the relationship be- highest frequency occurring when POT is between 0.8 tween the subsequent DSST along the TC track and the and 1.0, and few RW cases occur with POT less than 0.4 subsequent 24-h TC WR. All the fitted percentiles show (Fig. 4c). Compared with RW cases, SW cases are more

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FIG. 4. The frequency distributions (right ordinate) of SW (gray bar) and RW (black bar) cases and corresponding cumulative probability density (left ordinate, blue and red curves) against (a) Vmax, (b) SST, (c) POT, (d) DSST, and (e) translational speed (SPD). (f) The frequency distribution of SW (blue) and RW (red) cases against translational speed zonal (USPD; solid) and meridional (VSPD; dashed) components, respectively.

Unauthenticated | Downloaded 09/30/21 12:08 PM UTC SEPTEMBER 2020 F E I E T A L . 3703 evenly distributed over POT between 0.2 and 1.0. This and southerly flow of the RW and SW groups are present further confirms that the intense TCs with their inten- in the upper troposphere, while the difference in the 2 sities close to their upper limits are subject to greater lower troposphere is as small as 1.0–1.5 m s 1, especially potential for RW. The difference in frequency distri- for moderate POT. This implies stronger VWS in the bution between SW and RW cases is obvious with re- upper troposphere in RW cases. Previous studies have spect to DSST (Fig. 4d). A large amount (57.0%) of RW also shown that the upper-level VWS can ventilate the 2 cases occur in regions with DSST less than 218C day 1, warm core of a TC more efficiently (Gray 1968; Fu et al. while the majority (77.5%) of SW cases occur in DSST 2019). The upper-level VWS can also act to shrink the 21 greater than 218C day . The average DSST for the SW vertical extent of the axisymmetric vortex, reducing the 21 and RW cases is 20.818C and 21.768C day , respec- warm core and leading to TC weakening (Knaff et al. tively. The latter is slightly stronger than the average 2004). In addition, the slightly stronger lower- to mid- DSST for the onset of RW in the eastern North Pacific level VWS tends to enhance both the ventilation of the (21.08C) and the North Atlantic (21.58C), respectively midlevel vortex with dry environmental air and the (Wood and Ritchie 2015). flushing of low-entropy air into the frictional inflow layer In addition, most RW cases have SPD between 4 and (Tang and Emanuel 2010; Riemer et al. 2010, 2013). 21 8ms , while most SW cases have SPD between 2 and To estimate the extent to which VWS affects TC 21 6ms (Fig. 4e). About 53.5% of RW cases but only WR, we show in Fig. 6a the scatter diagram of TC WR 24.6% of SW cases occur when SPD is higher than 2 qagainstffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the deep-layer VWS, which is evaluated as 6ms 1. The higher SPD of RW cases results from both (U 2 U )2 1 (V 2 V )2, where the subscripts the higher USPD and VSPD (Figs. 4e,f). Note that al- 200 850 200 850 ‘‘200’’ and ‘‘850’’ indicate environmental U or V at 200 though USPD can be either westward or eastward for and 850 hPa, respectively. In general, all the 50th, 75th, both RW and SW cases, VSPD is mostly northward and and 95th percentiles of WR increase with increasing VWS. is higher for RW than for SW (Fig. 4f). The stronger TC WR is positively correlated with VWS (r 5 0.26) northward component of motion for RW implies that (Table 3), which is consistent with previous findings (Zeng the TC was moving into higher latitudes often with de- et al. 2007; Wang et al. 2015). The frequency distribution of creasing SST, which is consistent with the results shown 2 RW cases peaks at VWS about 10–12 m s 1 while that of in Figs. 3e and 3f. 2 SW cases peaks at VWS about 6–8 m s 1.TheRWcases 2 b. Environmental atmospheric factors with VWS stronger than 10 m s 1 account for 65.0% of all We first examine the vertical profiles of the composite RW cases, whereas the percentage is only 36.5% for SW 21 U and V over the TCs for SW and RW cases, respec- cases with VWS stronger than 10 m s (Fig. 6b). tively, conditional on TC POT (Fig. 5). POT represents Midlevel humidity is another factor that is often the potential of TC weakening, as discussed above. On considered to affect TC intensity and intensity change. average, the SW group is embedded in zonal wind with Most previous studies have mainly explored the influ- 2 easterly flow about 1–2 m s 1 below 850 hPa and west- ence of the azimuthal-mean RH (Kaplan and DeMaria 2 erly flow above, up to higher than 5 m s 1 in the upper 2003; Hendricks et al. 2010; Ma et al. 2019), while some troposphere (Fig. 5a), and uniform southerly wind studies show that the azimuthally asymmetric RH is 2 about 1–2 m s 1 throughout the troposphere (Fig. 5d). In more important to TC intensity change (Shu and Wu contrast, both U and V are much higher in the RW group, 2009; Wu et al. 2012) than only the azimuthal-mean RH. 2 with the maximum U and V higher than 9 m s 1 (Fig. 5b) Considering the close relationship between dry air in- 2 and 4 m s 1 (Fig. 5e), respectively, in the upper tropo- trusion and VWS (Tang and Emanuel 2010, 2012), we sphere. The stronger westerly in the upper troposphere and examined the correlations between TC WR and RHs easterly below 800 hPa imply stronger deep-layer westerly averaged vertically over 300–850 hPa and horizontally VWSinRWcases(Fig. 5b) than in SW cases (Fig. 5a). The over an annulus with 200- and 800-km radii from the stronger southerly wind in the upper troposphere also im- TC center in four quadrants with respect to the direc- plies stronger deep-layer VWS in RW cases (Fig. 5d)than tion of VWS (viz., the downshear-left, downshear-right, in SW cases (Fig. 5e). Note that the relatively stronger upshear-left, and upshear-right quadrants; Table 1), re- northerly appears for POT less than 0.65 in the RW group spectively. Results show that the RH in the upshear-left below 900 hPa, referring to TCs with moderate POT that quadrant (RHUL) has the highest negative correlation encounter the midlatitude westerly after their LMI. (r 520.26) with TC WR among the four quadrants, The differences in vertical wind profiles between while RHs in the other quadrants are not significantly the RW and SW groups can be more clearly seen from correlated with TC WR (Table 3). We also calculated Figs. 5c and 5f. Large differences in both the westerly RH averaged over different layers (such as between

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21 FIG. 5. The vertical distributions of environmental U winds (m s ) as a function of POT for (a) SW and (b) RW events and those of 2 environmental V winds (m s 1) for (d) SW and (e) RW events are shown. The differences in environmental U and V winds between (c) SW and (f) RW groups are shown.

400 and 700 hPa and between 850 and 700 hPa) and entropy in the eyewall and suppressing eyewall con- found that the 300–850-hPa RH has the highest corre- vection, thus leading to TC weakening. As we can see lation with TC WR. That is to say, low RHUL has a from Fig. 6c, which shows TC WR and various percentiles signiﬁcant negative effect on TC intensity and is likely against RHUL, WR exhibits an overall decreasing trend favorable for TC weakening. This is probably because with the increasing RHUL, which is more pronounced under the inﬂuence of VWS, midlevel environmental air when RHUL is less than 40%. The frequency distribu- is more likely to be transported into the TC eyewall from tions of SW and RW cases against RHUL (Fig. 6d)in- the upshear-left quadrant (Cram et al. 2007), lowering dicate that RW cases occur more frequently with RHUL

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FIG. 6. (left) As in Fig. 3, but for (a) deep-layer VWS (200–850 hPa), (c) relative humidity in the upshear-left quadrant (RHUL), and (e) divergence at 200 hPa (DIV200). (right) As in Fig. 4, but for (b) VWS (200–850 hPa), (d) RHUL, and (f) DIV200. lower than 35% while SW cases occur more frequently Therefore, we checked the relationship between TC WR with RHUL greater than 45%. and DIV200 with the results shown in Fig. 6e. It seems Large-scale divergence in the upper troposphere can that TC WR is positively correlated with DIV200, but the also inﬂuence TC intensity change (Hendricks et al. 2010). correlation is statistically insigniﬁcant with r 5 0.07 only

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(Table 3). The frequency of RW cases peaks at DIV200 2 2 around 2.5 3 10 6 s 1, and is generally greater than that in SW cases (Fig. 6f). This is consistent with the finding of Hendricks et al. (2010), who found that the composite upper-level divergence was the greatest in the composite of weakening TCs among all the TC intensity change groups (neutral, intensifying, rapid intensifying, and weakening). However, this result contradicts previous studies by Kaplan et al. (2010) and Lee et al. (2015), who found that stronger upper-level divergence provides better chance for a TC to intensify. Hendricks et al. (2010) proposed that this is mainly because weakening TCs are often interacting with upper-level troughs and are on average more intense and have larger extent of the upper-level outflow than neutral and intensifying FIG. 7. Relative importance of environmental factors used in the TCs. Therefore, DIV200 is still considered as a possible XGBoost model. Factors are listed to the left in descending order factor affecting TC WR in our analysis. of their relative importance. Description of these factors can be The above analyses demonstrate that 1) the TC WR is found in Table 1. positively correlated with Vmax and POT, the latter can represent the potential of TC weakening; 2) TC WR is the XGBoost model with the identified input factors can highly correlated with the storm SPD and SST gradient; well reproduce TC WR in the dataset. Note that the fitting and 3) the atmospheric factors, such as deep-layer VWS, error does not indicate the prediction error. To indicate RHUL, and DIV200, can also affect TC WR. Note that the model’s generalization (prediction) ability, a 100-fold these factors are not necessarily independent since some cross validation (CV) of the same model was further factors may correlate with each other significantly. Such carried out. The dataset was randomly divided into 100 dependence needs to be considered if any linear re- subsamples with equal size (about 30 cases), each of which gression model is to be developed. In the next section, was used as testing data with all the others pooled to- however, we apply the XGBoost method described in gether as training data in turn for once. The 100-fold mean 2 2 section 2, to quantify the relative importance of indi- RMSE of the prediction of testing data is 4.5 m s 1 day 1, vidual factors to TC WR and to examine the sensitivity which can be viewed as a measure of the model predic- of TC WR to these factors, by making full use of its tion performance. As a comparison, the fitting and CV capability to capture nonlinear relationships but little RMSEs for a counterpart multiple linear model fitted to 2 2 affected by the dependence among different factors. the same dataset are both around 5.0 m s 1 day 1.For predictive models, there is a ubiquitous trade-off between model bias and prediction variance (uncertainty), and 5. Relative contributions of individual factors to linear models have the property of high bias and low TC WR variance in general (Hastie et al. 2009, chapter 2). The above comparison suggests that the very small a. Model fitting and validation RMSE of the fitted XGBoost model is due to its capa- The XGBoost model described in section 2 is used bility of modeling nonlinearity, rather than overfitting to quantify the relative importance of factors to TC (otherwise the CV RMSE would have been much higher WR, including TC persistent factors (POT, USPD, and than that of the linear model). If used for prediction VSPD), DSST, and environmental atmospheric factors purpose, the CV RMSE could be reduced by tuning the (VWS, RHUL, and DIV200) identified in section 4 model parameters, with a cost of increasing the fitting (Table 3). These factors are used as input features to RMSE. In this work, however, the fitted model well the XGBoost model for all weakening TC cases. With captured the relationships between TC WR and the some typical parameter settings (learning rate h 5 0.3, factors of interest so that it serves as a powerful tool for minimum loss reduction g 5 0, and the maximum depth the analysis of relative importance of factors. of a tree 5 7; refer to https://xgboost.readthedocs.io/en/ b. Feature importance and sensitivity analysis latest/parameter.html for a detailed description), the root- mean-square error (RMSE) of the fitted TC WR stabilizes Figure 7 shows the relative importance of the identi- 2 2 2 at 9.6 3 10 4 ms 1 day 1 after about 600 iterations fied factors to TC WR, namely to what extent TC WR is (therefore, the number of trees K 5 600). This means that contributed by each of the input factors, by using the

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FIG. 8. The ICE plot of factors (a) POT, (b) DSST, (c) VWS, and (d) RHUL, respectively. Thin curves are XGBoost model-predicted WR as functions of one factor with all the other factors ﬁxed as observed from each individual sample. Thick curves are the 25th (blue), 50th (green), 75th (red), and 95th (black) percentiles of the predicted WR, respectively.

method described in section 2. We can see that POT is keeping all other features xc for each case unchanged as the most important factor in controlling TC WR, which the background. By varying xs within its value range for contributes 26.0% to TC WR. The rest are DSST each individual case, a set of the model-predicted re-

(18.3%), VWS (14.9%), RHUL (12.1%), USPD (11.8%), sponses can be obtained as a function of xs, conditional DIV200 (8.8%), and VSPD (8.1%), respectively. This is on the observed xc. Second, we plot all ICE curves for broadly consistent with the descending order of the cor- cases from each set of sensitivity experiments (thin relation coefficients shown in Table 3,exceptforUSPD curves in Figs. 8 and 9 ). Each curve reflects the pre- and VSPD, which could be due to their closely correla- dicted response to xs conditional on the observed xc for tions with DSST and VWS. each case. As we noted in section 2, these curves are In addition to the overall relative importance of in- zigzagged with a few remarkable jumps due to outlier dividual factors, we also examined the sensitivity and data. Therefore, we finally fit four percentiles (25th, variability of TC WR in response to the variation in each 50th, 75th, and 95th percentiles, thick curves) to all the factor by conducting several sets of sensitivity experi- curves, which are much more robust, to evaluate the ments based on the ICE method (section 2). First, we variability of predicted response to each factor (a set of choose a target feature xs (e.g., POT) to analyze, while experiments).

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FIG.9.AsinFig. 8, but for factors (a) USPD, (b) DIV200, and (c) VSPD, respectively.

Figure 8a shows the relationship between TC WR and the extremely unfavorable conditions, such as strong VWS POT for each weakening case in thin black curves and and/or sharp DSST, POT can cause a variability in WR by 2 2 the corresponding 25th, 50th, 75th, and 95th percentiles as much as 13 m s 1 day 1. The variability of WR, which of the WRs predicted by the model. The variability of is measured as the interquartile range between the 25th the curves reveals the extent of WR’s heterogeneity with and 75th percentiles, increases with increasing POT un- POT changing within its valid observational range, der the same environmental conditions. For example, the 2 2 which can be considered as the WRs of a weakening TC interquartile range increases from 3 m s 1 day 1 at POT 2 2 in a unique environment with different POTs. The pre- less than 0.4 to 6 m s 1 day 1 at POT around 1.0 (Fig. 8a). dicted WR increases with increasing POT and shows an The TC WR shows a general decrease with increasing approximately linear dependence on POT. Note that the DSST along the TC track (Fig. 8b). The predicted WR model also yields a few RW cases at POT below 0.5, decreases with increasing DSST for DSST larger than consistent with observations shown in Fig. 3. In partic- 228C but changes less for DSST smaller than 228C ular, the variation in the median of the predicted WR is (Fig. 4d). The median of WR decreases by about 2 2 2 2 2 2 2 2 about 9 m s 1 day 1 (from 4 to 13 m s 1 day 1) as POT 5ms 1 day 1 (from 11 to 6 m s 1 day 1) and the extreme 2 2 varies from 0.25 to 1.2, while that in the 95th percentile is WR (the 95th percentile) decreases by 5 m s 1 day 1 2 2 2 2 2 13 m s 1 (from 8 to 21 m s 1 day 1). This means that POT (from 20 to 15 m s 1 day 1) as DSST increases from 228 2 2 alone can induce a variability in WR by 9 m s 1 day 1 to 18C, meanwhile the interquartile range of WR de- 2 2 under the averaged environmental conditions, while under creases from about 7 to 5 m s 1 day 1.

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Consistent with previous studies, VWS is a major IBTrACS TC best track data and 6-hourly ERA-Interim factor leading to TC weakening. It can induce a variation reanalysis data during 1980–2017. A machine learning 2 2 in the median of WR by about 5 m s 1 day 1 (from 7 to approach, XGBoost, is used to quantify the relative im- 2 2 12 m s 1 day 1) for VWS in the observational range of portance of these factors to TC WR. In the WNP, an 2 0–16 m s 1 (Fig. 8c), which is considerably smaller than overwater TC weakening event can last up to 216 h that induced by POT, but is comparable with that in- (9 days) with an average weakening duration of 66.7 h. duced by DSST. All predicted percentiles of WR in- On average, RW TCs tend to have a weakening duration crease with increasing VWS when VWS is stronger than of about 82.0 h, which is much longer than that of 61.5 h 2 10 m s 1. This agrees with previously reported threshold for SW TCs. The average RW TC undergoes the RW 2 of about 10 m s 1 above which VWS can have a signifi- period for 36 h, which is comparable with the averaged 36 cant detrimental effect on TC intensity and intensifica- and 30 h in the eastern North Pacific and North Atlantic. tion (Zeng et al. 2007, 2008; Rios-Berrios and Torn The proportion of RW TCs to all TCs shows a distinct 2017). Note that the fitted 95th percentile of WRs is seasonal variation, with the maximum in November and 2 2 more than 16 m s 1 day 1 for any VWS, implying that the minimum in August. This suggests that RW occurs RW can even occur under weak VWS due to greater more frequently in fall than in summer in the WNP, which effects of other factors, such as large POT and negative could be due to the lower MPI resulting from the lower DSST, as shown in Figs. 8a and 8b. This is consistent SST in fall than in summer. with the estimated relative importance of the contrib- Statistical analysis shows that five factors are found to uting factors shown in Fig. 7. be positively correlated with TC WR (i.e., Vmax, POT, Compared with the sensitivity to POT, DSST, and VWS, USPD, and VSPD). Three other factors, includ- VWS, TC WR seems insensitive to the other environ- ing SST, DSST, and RHUL, are found to be nega- mental factors. Changes in TC WR against RHUL and tively correlated with TC WR. Second to POT, DSST, DIV200 are shown in Figs. 8d and 9b, respectively. SPD, VWS, and RHUL are also highly correlated with The median of the predicted WR changes by about TC WR, while DIV200 is statistically insignificant. 2 2 2ms 1 day 1 with either RHUL or DIV200. In addi- Consistent with the correlation analysis, a comparison tion, TC WR is also less sensitive to both USPD and between RW and SW cases indicates that RW cases 2 2 VSPD and changes by only about 3 and 2 m s 1 day 1 often occur with higher Vmax or POT, in regions with within their respective ranges of USPD and VSPD, re- lower SST and sharper SST gradient, and move farther spectively (Figs. 9a,c). The above results demonstrate eastward and/or northward than SW cases. RW cases that POT, DSST and VWS are important factors that often occur in stronger VWS and/or under greater upper- dominantly determine TC WR, and as a result, TC WR tropospheric divergence, and lower RHUL. A comparison is sensitive to these factors. Other factors are of sec- of the environmental U and V profiles between SW and ondary importance to WR. Although the linear corre- RW cases indicates that westerly wind in the upper tro- lations between TC WR and other factors may also be posphere and easterly wind below 800 hPa are stronger, comparable with those between TC WR and the domi- corresponding to stronger westerly VWS, in RW cases. nating factors, such as VWS, their effects are often not Note that as for the effect of midlevel RH on TC independent of the dominating factors. This partly ex- weakening in the WNP, our results are not in full plains why these factors are shown to be of secondary agreement with Ma et al. (2019). They found that the importance to TC WR. The application of XGBoost in role of environmental midlevel humidity is statistically this study shows that this model has advantages to avoid insignificant probably because of the lack of prevailing the feature interdependence issue and provides more midlevel dry-air layer over the WNP. Our results show accurate estimate of relative importance compared with that the RH in the upshear-left quadrant has a signifi- the widely used linear regression model, as well as to cant negative correlation with TC WR, while RHs in the provide an approach to sensitivity analysis. other quadrants are not significantly correlated with TC WR, suggesting that the midlevel dry air is more likely to be transported into the TC eyewall from the upshear-left 6. Conclusions and discussion quadrant of VWS, and thus leading to TC weakening. The overwater TC weakening is controlled by the un- The XGBoost model, a well-applied basic machine derlying ocean, large-scale atmospheric environmental learning algorithm, is adopted to quantify the relative conditions, and internal dynamical processes. In this importance of the above factors, and the ICE method is study, both the persistence and environmental factors used to conduct sensitivity experiments to examine the that affect the WR of overwater TCs in the WNP variability of TC WR in response to the variation of each are statistically analyzed and evaluated based on the factor. Results from these analyses confirm that POT is

Unauthenticated | Downloaded 09/30/21 12:08 PM UTC 3710 MONTHLY WEATHER REVIEW VOLUME 148 the most important factor among all the identified fac- data were downloaded from https://www.ncdc.noaa.gov/ tors and contributes 26.0% to TC WR. DSST, VWS, ibtracs/. The ERA-Interim data were downloaded from RHUL, USPD, DIV200, and VSPD contribute 18.3%, http://apps.ecmwf.int/datasets/. The authors thank the 14.9%, 12.1%, 11.8%, 8.9%, and 8.1%, respectively, to anonymous reviewers for their valuable comments and WR. These results are in good agreement with their suggestions. ranks of linear correlations with TC WR, except that USPD and VSPD seem not as important to TC WR as REFERENCES shown in the correlation analysis. This is most likely Bister, M., and K. A. Emanuel, 2002: Low frequency variability of because of their dependence on either DSST or VWS tropical cyclone potential intensity. 1. Interannual to inter- or both. The sensitivity experiments using the ICE decadal variability. J. 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